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Basic structural dynamics I
Wind loading and structural response - Lecture 10
Dr. J.D. Holmes
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Basic structural dynamics I
• Topics :
• e!ision o" single degree-o" "reedom !i#ration t$eory
• esponse to sinusoidal e%citation
Refs. : R.W. Clough and J. Penzien ‘Dynamics of Structures’ 1!"
R.R. Craig ‘Structural Dynamics’ 1#1
J.D. $olmes ‘Wind %oading of Structures’ &''1
• &ulti-degree o" "reedom structures ' Lect. 11
• esponse to random e%citation
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Basic structural dynamics I
(c −
)*uation of free +i,ration :
)(am-le : masss-ringdam-er system :
k
c m
(
'/((c(m =++
mass 0 acceleration s-ring force 2 dam-er force
- kx
- c(dx/dt)
=(m
/(.
e*uation of motion
• (ingle degree o" "reedom system :
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Basic structural dynamics I
• (ingle degree o" "reedom system :
)*uation of free +i,ration :
)(am-le : masss-ringdam-er system :
Ratio of dam-ing to critical c3cc :
k
c
m(
'/((c(m =++
m/ &
c=ζ
often e(-ressed as a -ercentage
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Basic structural dynamics I
• (ingle degree o" "reedom system :
Dam-er remo+ed :
k
m(4t5
)*uation of motion : '/((m =+
(m/( −=
is an e*ui+alent static force 4‘inertial’ force5(m −
6ndam-ed natural fre*uency :π
ω
&m
/
&7
1n 11 ==
Period of +i,ration8 9 :11
1&9
n==
ω
π
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Basic structural dynamics I
• (ingle degree o" "reedom system :
nitial dis-lacement ;o
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Basic structural dynamics I
• (ingle degree o" "reedom system :
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Basic structural dynamics I
• (ingle degree o" "reedom system :
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Basic structural dynamics I
• (ingle degree o" "reedom system :
Res-onse to sinusoidal e(citation :
)*uation of motion :tsin
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Basic structural dynamics I
• (ingle degree o" "reedom system :
+ritical damping ratio '
damping controls amplitude at
resonance
0.1
1.0
10.0
100.0
0 1 ,
n/n1
H ( n )
ζ/0.01
ζ/0.0
ζ/0.1ζ/0.,
ζ/0.
@t n3n1 1.'8 $4n15 13&ζ 9hen8 &/?<
('
ma( ≅
Dynamic am-lification factor8 $4n5
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Basic structural dynamics II
• esponse to random e%citation :
Consider an a--lied force =ith s-ectral density S
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Basic structural dynamics II
• esponse to random e%citation :
S-ecial case constant force s-ectral density S
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nd o" LectureJo$n Holmes
,,-0-234 JHolmes5lsu.edu
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